Towards a robust Terra [Elektronische Ressource] / von Markus Müller

TowardsarobustTerraDissertationzurErlangungdesakademischenGradesdoctorrerumnaturalium(Dr.rer.nat.)vorgelegtdemRatderChemisch-GeowissenschaftlichenFakultätderFriedrich-Schiller-UniversitätJena1vonMarkusMüllergeborenam16.10.1974inSondershausen1StaatsexamenfürdasLehramtanGymnasieninMathematikundPhysikGutachter:1. Prof.Dr.UweWalzer,InstitutfürGeowissenschaften,Friedrich-Schiller-UniversitätJena2. Prof.Dr.GerhardZumbusch,InstitutfürAngewandteMathematik,-UniversitätJenaTagderöffentlichenVerteidigung:11.02.2009AbstractInthisworkmantleconvectionsimulationwithTerraisinvestigatedfromanume-ricalpointofview,theoreticalanalysisaswellaspracticaltestsareperformed.Thestability criteria for the numerical formulation of the physical model will be madeclear.For the incompressible case and the Terra specific treatment of the anelastic ap-proximation, two inf-sup stable grid modifications are presented, which are bothcompatiblewithhangingnodes.FortheQ Q elementpairasimplenumerictestisintroducedtoprovethesta-1 1h 2hdiscbility for any given grid. For theQ P element pair and 1-regular refinements1 1h 2hwithhangignodesanexistinggeneralproofcanbeadopted.The influence of the slip boundary condition is found to be destabilizing. For theincompressiblecaseacurecanbeadoptedfromtheliterature.The necessary conditions for the expansion of the stability results to the anelasticapproximationwillbepointedout.